Attendees at a rally for former President Donald J. Trump in Schnecksville, Pa., this month. Michelle Gustafson for The New York

This month, The New York Times/Siena College poll asked voters how much they think former President Trump respects women: a lot, some, not much or not at all?

You’ll never guess what happened next!

A majority of men — 54 percent — said that Trump respects women either “a lot” or “some.” Just 31 percent of women saw things that way.

Trump, a man known for bragging about grabbing women’s private parts — and on trial in connection with the cover-up of a sex scandal involving a porn star — has long symbolized a kind of machismo that to many people reads as misogyny.

But that disparity is important to understand in an election that already seems primed to turn on the question of just how big the gender gap between Trump, who draws more support from men, and President Biden, who leads among women, is going to be. Our poll found that Trump had a 20-percentage-point lead among men, while Biden had a 16-percentage-point lead among women.

“The formula for any Democrat in a close race is to win women by more than they lose men, and frankly, right now we’re behind,” said Celinda Lake, a Democratic pollster for Biden’s 2020 campaign. “Having women become as intensely anti-Trump as men are pro-Trump is really, really important.”

The perception of Trump’s respect for women is a rare example of his standing with voters decreasing in recent years. Times polling has found that voters view Trump more positively on issues like his handling of the economy and law and order than they did in 2020.

But on the matter of whether Trump respects women, he has actually fallen a small amount, four percentage points, since the poll last asked the question in 2016.

And that could be a harbinger of how voters’ views of Trump might change as he draws more news coverage, since his treatment of women has figured prominently in the headlines for months. There were the January proceedings of the civil defamation trial in which Trump was ordered to pay $83 million in damages to a woman who accused him of rape. He disparaged Nikki Haley, who was then running for the G.O.P. presidential nomination, by making fun of her dress and calling her “birdbrain.” And now he’s in court over a sex scandal.

“The fact that it’s gelled that much to show up in the numbers is really surprising,” Lake said.

Men are from Mars

I called Ryan Canaday, 42, one of the many men who told our pollsters that Trump has “a lot” of respect for women. He knows Trump is accused of having covered up a hush money payment to a porn star. And Canaday, who works in Ohio’s booming construction sector and said he is an independent voter, is not bothered one bit.

“I absolutely think he did that. I think it’s what he’s done his entire life,” Canaday, who plans to vote for Trump this fall, said. “Realistically, if I had the kind of money that would shut people up, I would be throwing it at a lot of people.”

Trump’s enduring strength with male voters like Canaday is one of his brightest data points. He has the support of 57 percent of men, according to our most recent poll, and only 28 percent of men think he does not respect women at all.

Canaday thinks it’s not necessarily disrespectful to have an affair — which Trump denies — with a consenting adult. And, what’s more, he thinks Trump’s experience in the business world had likely bolstered his respect for women. “He’s a developer,” Canaday said. “Real estate, as a whole, is predominantly women-run.” (The National Association of Realtors says that, while more real estate agents are women, they are less represented in commercial real estate and in executive roles.)

Casey Bates, 49, a chef from Michigan who is planning on voting for Trump, also pointed to Trump’s personal staffing choices to back up his belief that Trump has lots of respect for women.

“He’s said bad things about certain women, but he’s also appointed them to high positions,” Bates said, recalling how Trump had some female press secretaries while he was president.

At the risk of asking an obvious question, I called Whit Ayres, a Republican pollster, to ask him why he thought men were so much more likely than women to view Trump as being respectful toward the opposite sex.

“The best explanation for that is, men are from Mars, women are from Venus,” Ayres said, adding that the best way for Trump to improve his standing in the eyes of female voters was simply to “change the subject.”

Will more women turn toward Biden?

Women are more likely to be Democrats, so part of the gender gap between Trump and Biden is probably explained by existing partisanship, rather than anything particular about the way they see Trump.

But, interestingly, the divide in how women and men view Trump in terms of his respect for women persists even when you look at Republicans alone. Our pollsters found that 85 percent of Republican men believe Trump respects women, while 72 percent of Republican women believe that to be the case. And there is some interest in Biden among Republicans who don’t think Trump respects women, they found.

Take Riley Glissendorf, 21, who said she is a registered Republican who lives in Missouri. Glissendorf agrees with Trump’s “America First” approach to foreign policy, but she describes herself as liberal on many other issues and intends to vote for Biden in the fall — partially because of Trump’s use of “disrespectful, demeaning, unkind” language toward women and his role in rolling back abortion rights by appointing three of the Supreme Court justices who voted to overturn Roe v. Wade.

“First and foremost, I’m a woman,” Glissendorf, who works in a bookstore, said. “I couldn’t bring myself to vote for anyone who not only doesn’t respect me politically, but doesn’t respect me as a person.”

Democrats are hoping that their renewed focus on issues like abortion rights and subsidies for child and family care might help to expand the gender gap in their favor. They need anti-Trump voters just as much as they need Biden supporters.

They have one in Brittany Lombardo, a 38-year-old acupuncturist from Georgia. She is intrigued by the environmental activism of Robert F. Kennedy Jr., the independent presidential candidate, but says she plans to vote for Biden in November because she sees that as the best way stop Trump.

“I don’t think he respects women,” Lombardo said of Trump. “Republicans in general think of women as a vessel and want to go back to the ’50s. Do I want that? No.”

                  The U.S. Supreme Court is set to hear arguments Thursday on whether former President Donald J. Trump is immune from prosecution on charges of plotting to overturn the 2020 election. Haiyun Jiang for The New York Times

What to listen for at Trump’s immunity hearing

Tomorrow, the Supreme Court will take up Trump’s claim of presidential immunity, addressing a big question about presidential power. It will also probably determine whether or not Trump faces a trial for trying to overturn the last election before the next one. I asked my colleague Adam Liptak, who covers the Supreme Court for The Times, to tell us what to listen for. Our conversation was edited for length and clarity.

JB: What’s so important about this hearing tomorrow?

AL: In a legal sense, it asks the court to decide an untested question of whether a former president can be prosecuted for official conduct, which the special counsel Jack Smith argues is possible. The practical question, though, is whether the court will rule quickly and cleanly enough for Smith to bring Trump to trial before the 2024 election.

JB: Help us listen with expert ears. What kinds of questions from the justices will we hear if things are going well for Trump? And for Smith?

AL: I expect things to go well for Smith, as a general matter. It would be a surprise if the court were to adopt the broadest form of President Trump’s claim, which is essentially that presidents are above the law.

But the only way Smith can get this to trial in the coming months is if he gets a clean win, and if he gets it soon. So what you want to be listening for is how complicated the justices think the question is — how much they think there are distinctions to be drawn on what counts as official and unofficial conduct, and on the question of immunity itself.

JB: Are you saying it could be possible for Smith to win on the bigger question of whether or not a president is above the law, but still not be able to try Trump before the election?

AL: If Smith gets a complicated win, one that sends it back to the lower courts to do more work, draw more distinctions, perhaps even be subject to further appeals, the practical question of whether this trial can get done before the election evaporates. And if the court waits until the end of its term in June to issue its decision, even one categorically rejecting everything Trump says won’t guarantee the trial can take place before the election.